When building energy efficient buildings, there are three main areas to address to make your building perform better:                First is to stop “thermal bridging” caused by a lack of insulation. Heat energy transfers through wood framing members thus making a wall system very inefficient.        Second is air tightness. When a building is not airtight, incoming drafts bring in undesired temperatures with airflow. This undesired airflow can also bring in unhealthy air while traveling by or through wall areas that have been subject to moisture issues.        Third is water management, both as to shedding bulk water and letting trapped moisture escape.        
The use of exterior insulation is a great and cost effective way to handle all three of foregoing items when done properly. There is a weak point with rigid insulation at the openings of windows and doors, however. General practices teach to build one's access (i.e., window or door) openings wider than the rough opening. The window/door can then be framed out with wider lumber to meet the additional depth of insulation at the attachment points for these windows and doors. While doing a good job of making an anchor point for the access (windows and doors) areas, wood framing makes for a very week point for insulation. Such points are called thermal bridges. At these thermal bridge points, cool air escapes through conduction in the summer while also letting cold air into your house in the winter.
At these same thermal bridge points, there is often a moisture management problem. See especially FIG. 1—PRIOR ART. Wood (or lumber) frame surrounds become a dew collection point causing unwanted condensation. That condensation accrues on the outside of a structure in the summer for promoting fungus, mold, mildew, and rot. In the winter, moisture problems often occur inside the structure. In addition, condensations like these contribute to airborne contaminants that the structure occupants breathe.
Known insulation systems include, but are not limited to: the releasable/re-attachable window frame insulation system of Sahadeo et al. U.S. Pat. No. 8,479,462; the “adhearable” window insulation material of Shippen U.S. Pat. No. 5,108,811; the gasket driven window insulation approach of Ahonen U.S. Pat. No. 4,624,077; and Bauch's Removable Insulation System per U.S. Pat. No. 4,486,990. Internationally, there is also known the thermal insulation window structure of Foster Canadian Patent No. 1,275,200 and WIPO No. 2014/033,231 to Soudal.